Video: Pack 3 • Paper 1 • Question 5

Pack 3 • Paper 1 • Question 5

03:19

Video Transcript

Sarah is filling bags with rice. The capacity of each bag is two-thirds of a cubic decimeter. The mass of rice is 1.45 kilograms per cubic decimeter. Work out the total mass of 30 bags filled with rice. The mass of the bags can be neglected.

Now, try not to worry too much about the terminology here. A cubic decimeter is a measure of volume. 1000 cubic decimeters are equal to one cubic meter. However, we are given the mass per single cubic decimeter. So we just need to deal with these.

Let’s begin by working out the mass of a single bag of rice. We’re told that the mass is 1.45 kilograms per cubic decimeter. We can write this as a ratio. For every 1.45 kilograms of rice, its volume is one cubic decimeter. The capacity of each bag though is only two-thirds of a cubic decimeter. To scale the right-hand side of our ratio to two-thirds, we can simply multiply it by two-thirds since one multiplied by two-thirds is two-thirds. Since this is a ratio, we must also do this to the left-hand side.

The mass of a single bag of rice is given by two-thirds multiplied by 1.45 kilograms. This isn’t a particularly nice calculation to complete in our heads. So we’ll leave it in this form for now. To find the mass of 30 bags of rice, we’ll need to multiply this value by 30. That’s 30 multiplied by two-thirds multiplied by 1.45.

Since multiplication is commutative, that means it can be completed in any order. We can start by multiplying 30 by two-thirds. If we write 30 as 30 over one, we can cross cancel by dividing both 30 and three by three. That gives us 10 over one multiplied by two over one. 10 multiplied by two is 20 and one multiplied by one is one. 20 over one is simply 20.

We need to calculate then 20 multiplied by 1.45. 20 is the same as two times 10. So we’ll start by multiplying 1.45 by two. We could do this in our head or use a formal written method. Let’s start by looking at the column method.

Five multiplied by two is 10. So we put a zero in this column and carry the one. Four multiplied by two is eight. And then, when we add that one, we get nine. Since only one of the numbers is a decimal, we can carry the decimal point directly below the one in our question. And then, one multiplied by two is two. 1.45 multiplied by two is, therefore, 2.9. Finally, we’ll multiply 2.9 by 10. When we multiply by 10, we move all of the digits to the left one space. 2.9 multiplied by 10 is, therefore, 29.

The total mass of 30 bags filled with rice is then 29 kilograms.

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